MANAGEMENT SCIENCE INDIVIDUAL PROJECT formulate a linear programming model and write down the mathematical model for this problem

i = A,B,C,D,E,F Consultants j = 1,2,3,4,5,6,7,8 Projects Objective is to maximize utilization of consultant skills and meeting clients’ needs based on ratings.. If the company want to ma

UEH UNIVERSITY COLLEGE OF BUSINESS SCHOOL OF INTERNATIONAL BUSINESS AND

MARKETING

MANAGEMENT SCIENCE INDIVIDUAL PROJECT

Subject: Management Science

Class ID: 21C1BUS50304001

Lecturer: Ph.D Ha Quang An

MARK LECTURER’S COMMENT

Question 1: …………

Question 2: …………

Question 3: …………

Sum: ………

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LECTURER’S SIGNATURE

(Full Name and Signature)

Ha Quang An

TABLE OF CONTENT

Linear Programming 2

Question a 2

Question b 4

Question c 4

Question d 5

Question e 5

Question f 6

Decision Making 8

Forecasting 10

Question a 10

Question b 10

Question c 10

Question d 11

1 Linear Programming

a Formulate a linear programming model and write down the mathematical model for this problem

Decision variables are number of hours assigned to each consultant for respective project

i = A,B,C,D,E,F (Consultants)

j = 1,2,3,4,5,6,7,8 (Projects)

Objective is to maximize utilization of consultant skills and meeting clients’ needs based on ratings This can be accomplished by maximizing the product of the number of hours assigned and the ratings Since higher ratings are better, maximize the objective

F 8

∑ ∑

R x (xij)

Maximize Z =

i− A j=1

Where Z is the ratings adjusted hours and R is the rating provided

Subject to constraints:

Hours availability:

8

∑

Consultant A:

Consultant B:

Consultant C:

Consultant D:

Consultant E:

x Aj < 450

x Bj < 600

xCj < 500

x Dj < 300

x Ej < 710

j=1

8

2

∑

j=1

Project hours:

F

∑

Project 1:

Project 2:

Project 3:

Project 4:

Project 5:

Project 6:

Project 7:

Project 8:

xi 1 = 500

i= A

F

∑xi 2 = 240

xi 3 = 400

xi 4 = 400

xi 5 = 350

xi 6 = 460

xi 7 = 290

xi 8 = 200

i= A

F

∑

i= A

F

∑

i= A

∑

Project 4:

Project 5:

Project 6:

Project 7:

Project 8:

x × (Hourly Rate) < 90,000

i 4

i i= A

F

∑x × (Hourly Rate) < 65,000 i 5 i

i= A

F

∑x × (Hourly Rate) < 85,000 i 6 i

i= A

F

∑x × (Hourly Rate) < 50,000

4

c If the company want to maximize revenue while ignoring client preferences and

consultant compatibility, will this change the solution in B?

When the company maximize revenue while ignoring client preferences and consultant

compatibility, the solution in B will change

d Create a sensitivity report What is the shadow price in this case?

e If consultant A and E change their hourly wage from $155 to $200 (A) and from $270 to

200, will the solution change?

$

When consultant A and E change their hourly wage from $155 to $200 (A) and $270 to $200, the solution will change

f By experience,

consultant B and E

is getting better at

their ability, which mean their capacity for every project now minimum start from 3

instead of 1 or 2, will the shadow price change?

The shadow price will not change

The shadow price of Q.F:

The shadow price of Q.B:

2 Decision making

8

EMV of Local gas company ¿60%× 300.000+40%× 150.000=240.000

The maximum profit is related to Locas gas company, so the decision must be Locas gas

company

3 Forecasting

a Weighted Moving Average Method

The weight of April is 0.4

The weight of May is 0.2

The weight of June is 0.4

10

b 3-month average method

c Exponential Smoothing

3

The forecast for June is 16 and ∝=0.4

The forecasting demand for July

¿

¿

DJune × ∝+FJune ×(1−∝)

18×0.4+16×(1−0.4)=16.8

d Weighted Moving Average Method averages the data for only the most recent time periods

with the weight factor of 0,4; 0,2; 0,4

3-month average method averages the data of 3 lastest months

Exponential Smoothing modifies the moving-average method by placing the greatest weight on the last value in the time series and then progressively smaller weights on the older values This formula for forecasting the next value in the time series combines the last value and the last forecast (the one used one time period ago to forecast this last value)

For me, the best and most accurate is 3-month average method Because, the moving-average method is somewhat slow to respond to changing conditions and Exponential Smoothing

choosing the value of ∝ amounts to using this pattern to choose the desired progression of

weights on the time series values